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NSW SelectiveYear 7 entry

Algebra for the Selective maths test

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Algebra in the Selective maths test means finding a hidden number. Your child treats each equation as a balance: name the unknown, do the same thing to both sides, then check the answer in the question.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Algebraic Thinking (lesson preview)

A short preview from the SelectiveReady lesson “Algebraic Thinking”, on algebra for the NSW Selective test.

Published:

Read the video transcript

Now for step 2, where we build and test our rule. Since everything is going up by 3, our rule probably involves multiplying by 3. So let's try it with the first pair. If we take our input 1 and multiply it by 3, we get 3. Hmm, but we need the output to be 4. So what's missing? We need to add 1. Let's see if that's our rule. Multiply by 3, then add 1. Let's test it. 1 times 3 is 3, plus 1 is 4. Yes, it works for the first pair, but we have to check the others. 2 times 3 is 6, plus 1 is 7, it works again. We found it. That's our rule. And now for the final satisfying part, step 3. We just apply our proven rule to the number we're trying to solve for, which is 4. So we take 4, multiply by 3, which is 12, then we add 1, and we get 13. Case closed. The answer is 13.

Algebraic Thinking is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The preview plays here with English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns to treat algebra as a mystery. The letter is a suspect hiding a number, and the equation is the case file that holds the clues. They'll be able to keep an equation balanced, find a two-step rule in a table and test that rule on every pair.

The clip builds the rule "multiply by three, then add one" and uses it to finish a table. The full lesson adds the balance scale, the biggest trap and a recap.

3

How does algebra show up in the Selective maths test?

Algebra sits inside the Mathematical Reasoning section, mixed with other topics. The Department publishes no topic list: it says questions come from a range of maths content areas2NSW Education · 13 October 2026 · Published.

PartThe Department's rule
Questions352NSW Education · 12 October 2026 · Published, each with 52NSW Education · 12 October 2026 · Published options
Time402NSW Education · 12 October 2026 · Published minutes
CalculatorNo calculator2NSW Education · 12 October 2026 · Published
Working paper23NSW Education · 12 October 2026 · Published sheets, and more on request
Wrong answersThe practice papers say there are no marks lost for incorrect answers4NSW Education · 13 October 2026 · Published

In these questions the unknown is rarely written as x. It shows up as a bag on a set of scales, a missing price, a number puzzle or a table with a rule. Questions draw on concepts from the NSW curriculum up to Year 62NSW Education · 12 October 2026 · Published, so your child doesn't need indices, function notation or simultaneous equations. 2NSW Education · 12 October 2026 · Published

4

What is algebraic thinking?

Algebraic thinking is working with a number you don't know yet. A letter or an empty box stands in for it, and an equation says that two amounts are equal. In Year 5 and Year 6 it also means spotting a pattern and saying its rule.

In wordsIn symbols
A number plus seven makes fifteenx + 7 = 15
Three times a number is twelve3 × n = 12
Five less than a number is ninen − 5 = 9
Double a number, then add one, makes eleven2 × n + 1 = 11
5

What is the method for algebra questions?

The lesson's golden rule is the balance: whatever you do to one side, do to the other. Picture the equals sign as the middle of a set of scales.

Keep the scales balanced: name the unknown, write the balance, make the same move on both sides, then check in the question.

  1. Name the unknown

    Give the hidden number a letter or a box. Say in words what it stands for: the mass of one bag, or the price of one drink.

  2. Write the balance

    Turn the words into an equation, piece by piece. What's on the left must equal what's on the right.

  3. Same move on both sides

    Undo the last step first. Take away what was added, then share out what was multiplied, on both sides each time.

  4. Check in the question

    Put the answer back into the words, not just the equation. If every clue fits, the case is closed.

What about a table with a rule?

The clip's question is an input and output table. The same detective plan works on any of them.

  1. Find the pattern

    Look down the outputs only. If they go up by the same amount each time, the rule probably multiplies by that amount.

  2. Build the rule, then test it

    Try the multiply part on the first pair and see what's missing. Then test the full rule on every pair, not just the first.

  3. Apply it

    Use the tested rule on the input the question asks about.

6

What does a worked algebra example look like?

We wrote this question to show the four steps.

Our practice question
Ava thinks of a number. She multiplies it by 4, then adds 9. Her answer is 37. What was her number?
A. 4 · B. 7 · C. 9 · D. 11 · E. 28
StepWhat your child does
Name the unknownAva's number is n.
Write the balance4 × n + 9 = 37
Undo the last stepTake 9 off both sides: 4 × n = 28
Undo the first stepShare both sides by 4: n = 7
Check in the question7 times 4 is 28, and 28 plus 9 is 37. The answer is B.

Option E is the trap. It is four times Ava's number, one step short of the answer.

7

Which mistake catches most children in algebra?

The biggest trap in the lesson is a rule that's too simple. In the clip's table, 1 becomes 4, so "add three" looks right, but 2 becomes 7, not 5.

TrapWhat it looks likeThe fix
A rule that only fits once"Add three" works for the first pair and fails the secondTest the rule on every pair
One side onlyTaking 9 off the left of the balance but not the rightSame move on both sides, every time
"Less than" backwardsFive less than a number put down as 5 − nTry a real number first: five less than twelve is seven
8

Can my child try one on their own?

Here is a balance question from our free maths set. Your child answers it, then checks the steps below.

Practice question · SEL-MA-TST-10

Anjali's scales are balanced. Every bag of rice has the same mass.

What is the mass of one bag of rice?

  1. A

    150 g

  2. B

    160 g

  3. C

    175 g

  4. D

    200 g

  5. E

    600 g

Show answer and explanation

Answer: D

Answer: D (200 g)

  1. Take one bag off each side. The scales still balance: 3 bags and 100 g on the left, 700 g on the right.
  2. Take 100 g off each side: 3 bags = 600 g.
  3. One bag: 600 ÷ 3 = 200 g.

Why the other options are wrong

  • A (150 g): This shares 600 g among 4 bags, forgetting to take a bag off the left to match the bag on the right.
  • B (160 g): This adds all the masses (800 g) and shares them among all 5 bags, but the bags are on opposite sides.
  • C (175 g): This shares the 700 g among the 4 bags on the left and ignores the 100 g weight and the bag on the right.
  • E (600 g): This is the mass of 3 bags together, not one bag.

  1. Name the unknown

    The mass of one bag of rice. The left pan has 4 bags and 100 g, and the right pan has 1 bag and 700 g.

  2. Same move on both sides

    Take one bag off each side: 3 bags and 100 g balance 700 g. Take 100 g off each side: 3 bags weigh 600 g.

  3. Share and check

    One bag is 600 ÷ 3 = 200 g, so the answer is D. Option A, 150 g, forgets the bag on the right pan.

9

How can my child practise algebra at home?

Short puzzles said out loud work well. Each one uses the balance or the rule test.

I'm thinking of a number

Take turns: multiply a secret number, then add or subtract. The other person works backwards to find it.

Draw the scales

Sketch scales with boxes and weights. Take the same thing off both pans until one box is left alone.

Guess my rule

One person picks a secret two-step rule. The other gives inputs and must test a rule on three pairs before saying it.

10

Questions parents ask about algebra for Selective

Does my child need to know algebra with x?

Not the high school kind. The unknown usually appears as a box, a bag or a price. Working backwards, undoing each step in reverse order, solves most questions.

Can my child use a calculator?

No. No calculator2NSW Education · 12 October 2026 · Published is allowed in any section, so practise the sharing and undoing on paper.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Mathematical Reasoning →Lesson: Patterns & Rules →Lesson: Number Operations Mastery →Lesson: Fractions, Decimals & Percentages →Free Selective practice test →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Placement test

    NSW Department of Education · Checked 12 October 2026 · CC BY 4.0 (NSW Department of Education copyright notice); quotes credited

  4. Selective High School Placement Test, Thinking Skills Question Paper, Practice Test 1 (2026 entry practice tests, PDF)

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Quoted briefly with credit. Saved text: the cover-page instructions only; the question pages are not stored (W§3.22).

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